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The study of the punching cards mechanism with SolidWorks
Motion
Dorian Nedelcu, Gilbert-Rainer Gillich, Istvan Biro, Zoltan-Iosif
Korka, Attila Gerocs
The objective of the paper is to calculate the velocities and
accelerations for some points of the punching cards mechanism and to
compare the results calculated through grapho-analytical method with
the SolidWorks Motion results.
Keywords: Mechanism, punching cards, SolidWorks Motion
1. Introduction
A punched card is a simple piece of paper stock which was widely used in the
last century in computers or machines organized as semiautomatic data processing
systems [1], [2]. They contain digital information represented by the presence or
absence of holes in predefined positions.
The punching cards mechanism transforms the circular movement of the
leading element OA into a translation of the driven element point M. The kinematic
parameters of the mechanism are the linear velocities and accelerations.
The aim of the present paper was to assess the grapho-analytical method and
the facilities of the Motion module from SolidWord (SW) software for the
kinematic calculus of the main points of a punching card mechanism.
2. The geometry and main parameters of the punching cards mechanism
The geometry of the punching cards mechanism presented in Fig. 1 is
composed from three beams OA=0.2 m, AB=0.5 m, DM=0.4 m and one triangle
BCD with BC=CD=0.35 m and BD=0.55 m. The length of OC distance is
OC=0.45 m. The punching cards mechanism is driven by a Rotary Motor applied
to the OA beam with constant rotational velocity n1=191 rot/min equivalent with
the angular velocity ω1=20 rad/s which corresponds to 1145.9 degree/second. The number of rotations during 1 sec is 3.18 and the time of one rotation is 0.314 sec.
The rigid angle α=150o between X direction and OC beam is constant. The start
ANALELE UNIVERSITĂŢII
“EFTIMIE MURGU” REŞIŢA
ANUL XXVI, NR.1, 2019, ISSN 1453 - 7397
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position of the mechanism is defined by 210o angle between X direction and OA
beam. The analysis time of the study was imposed 1 sec. The point M move only
along Y direction and point C is fixed. The point O of the OA beam is connected to
Fixed part 1 and the point C of the CD beam is connected to Fixed part 2. This
study aims to compare the velocities and accelerations of A, B, D and M points,
calculated by grapho-analytical method and SolidWorks Motion module.
Figure 1. The punching cards geometry
3. Theoretical background and numerical results
The kinematic schema of the starting position mechanism was represented on
the k1=1/100 [ ] scale, Fig. 2 [3]. For the calculation of the velocities the kv =
ω1 k1 = 1/5 = 0.2 [ ] coefficient was used [3]. For the calculation of the
accelerations the kA = ω1 kv = 4 [ ] coefficient was used [3]. The velocities
and accelerations are calculated only for the start position of the mechanism by
grapho-analytical method through equations (1) ÷ (8) [3].
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Figure 2. The kinematic schema of the starting position mechanism
VA= ω1∙LOA; VA=20∙0.20 = 4 m/s (1)
�� � �� ∙ ��� �1
5 ∙ 18 � 3.6�/� (2)
�� � �� ∙ ����1
5 ∙ 18 � 3.6�/� (3)
�� � �� ∙ ����1
5 ∙ 14 � 2.8�/� (4)
�� � ��� ∙ !� � 20
� ∙ 0,2 � 80�/�� (5)
�� � �$ ∙ �$� � 4 ∙ 15,2 � 60.8�/�� (6)
�� � �$ ∙ �$�� � 4 ∙ 15,5 � 62�/�� (7)
�� � �$ ∙ �$��; �� � 4 ∙ 26 � 104�/�� (8)
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4. The stages of Motion Study
The stages of the study are as follows [4] and [5]:
o Activation of the SolidWorks Motion module; o Creation and specification of the study’s options; o Specify Rotary Motor; o Specify Motion Mates; o Running the design study.
To specify Rotary Motor click Motor to create a new rotary motor; select the
face of the OA beam select Constant speed from Motor Type list and set 191 rpm
value in the speed motor field; click � and the Rotary Motor1 branch will be
created in the MotionManager design tree (Figure 4).
The mates indicated in Table 1 will be applied in Motion Study between the
assembly components. The mate Mate7 was only necessary to specify the
initial position of the mechanism, but before the motion analysis calculation
this mate must be suppresses.
Table 1. The mates applied to the punching cards mechanism
Mate
name
Mate
type
Component 1 Component 2
Mate1 Coincident Point O - Fixed part 1 Point O - beam OA
Mate2 Coincident Point A - beam OA Point A - beam AB
Mate3 Coincident Point C - Fixed part 2 Point C - beam CD
Mate4 Coincident Point B - beam AB Point B - beam DB
Mate5 Coincident Point D - beam DM Point D - beam CD
Mate6 Coincident Point M - beam DM Y direction
Mate7 Angle=210o X direction OA beam
5. Simulation and theoretical results comparison
For grapho-analytical method the velocities and accelerations were
calculated only for the start position of the mechanism, while in SolidWorks
Motion the results are calculated for the whole time of the study. The results
are presented as charts in Fig. 3 ÷ Fig. 10 and numeric in Table 2 and 3.
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Figure 3. The velocity of point A
Figure 4. The velocity of point B
3.0
3.2
3.4
3.6
3.8
4.0
4.2
4.4
4.6
4.8
5.0
0.0 0.2 0.4 0.6 0.8 1.0
Velocity point A
[m/sec]
Time [sec]
SolidWorks Motion
Grapho-analytical
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0.0 0.2 0.4 0.6 0.8 1.0
Velocity point B
[m/sec]
Time [sec]
SolidWorks Motion
Grapho-analytical
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Figure 5. The velocity of point D
Figure 6. The velocity of point M
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0.0 0.2 0.4 0.6 0.8 1.0
Velocity point D
[m/sec]
Time [sec]
SolidWorks Motion
Grapho-analytical
0.0
2.0
4.0
6.0
8.0
10.0
12.0
0.0 0.2 0.4 0.6 0.8 1.0
Velocity point M
[m/sec]
Time [sec]
SolidWorks Motion
Grapho-analytical
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Figure 7. The acceleration of point A
Figure 8. The acceleration of point B
60
65
70
75
80
85
90
95
0.0 0.2 0.4 0.6 0.8 1.0
Acceleration
point A [m/sec]
Time [sec]
SolidWorks Motion
Grapho-analytical
0
50
100
150
200
250
0.0 0.2 0.4 0.6 0.8 1.0
Acceleration
point B [m/sec]
Time [sec]
SolidWorks Motion
Grapho-analytical
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Figure 9. The acceleration of point D
Figure 10. The acceleration of point M
0
50
100
150
200
250
300
0.0 0.2 0.4 0.6 0.8 1.0
Acceleration
point D [m/sec]
Time [sec]
SolidWorks Motion
Grapho-analytical
0
50
100
150
200
250
300
350
400
450
0.0 0.2 0.4 0.6 0.8 1.0
Acceleration
point M [m/sec]
Time [sec]
SolidWorks Motion
Grapho-analytical
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Table 2. Numerical results from SolidWorks Motion
Time VA VB VD VM aA aB aD aM
sec m/s m/s m/s m/s m/s2 m/s2 m/s2 m/s2
0.00 4.00 3.45 3.45 2.74 80.01 60.83 60.83 95.36
0.04 4.00 4.11 3.45 5.60 79.30 60.83 60.83 27.50
0.08 4.00 3.21 3.45 4.37 80.06 60.83 60.83 78.85
0.12 4.00 1.41 3.45 1.35 79.99 60.83 60.83 57.47
0.16 4.00 0.53 3.45 0.46 80.10 60.83 60.83 44.23
0.20 4.00 3.03 3.45 3.63 80.18 60.83 60.83 143.27
0.24 4.00 7.31 3.45 9.80 79.95 60.83 60.83 39.21
0.28 4.00 0.83 3.45 0.41 72.16 60.83 60.83 97.07
0.32 4.00 3.71 3.45 3.29 80.02 60.83 60.83 93.67
0.36 4.00 4.05 3.45 5.72 80.03 60.83 60.83 10.09
0.40 4.00 2.99 3.45 3.90 79.78 60.83 60.83 80.02
0.44 4.00 1.13 3.45 1.03 80.10 60.83 60.83 52.26
0.48 4.00 0.82 3.45 0.73 80.03 60.83 60.83 48.96
0.52 4.00 3.56 3.45 4.55 80.22 60.83 60.83 171.32
0.56 4.00 7.52 3.45 9.15 80.29 60.83 60.83 180.23
0.60 4.00 0.41 3.45 0.20 77.82 60.83 60.83 88.71
0.64 4.00 3.89 3.45 3.83 80.01 60.83 60.83 88.73
0.68 4.00 3.97 3.45 5.72 80.00 60.83 60.83 8.37
0.72 4.00 2.74 3.45 3.40 79.98 60.83 60.83 83.10
0.76 4.00 0.84 3.45 0.75 79.99 60.83 60.83 47.09
0.80 4.00 1.13 3.45 1.04 80.03 60.83 60.83 56.32
0.84 4.00 4.15 3.45 5.61 80.20 60.83 60.83 194.01
0.88 4.00 7.28 3.45 7.70 91.17 60.83 60.83 381.19
0.92 4.00 1.40 3.45 0.71 79.86 60.83 60.83 84.53
0.96 4.00 4.01 3.45 4.33 80.01 60.83 60.83 80.89
1.00 4.00 3.86 3.45 5.62 80.01 60.83 60.83 26.67
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Table 3. Numerical results comparison
Parameter Time VA VB VD VM aA aB aD aM
Units sec m/s2 m/s
2
Grapho-
analytical 0.00 4.00 3.6 3.6 2.8 80 60.8 62 104
SW Motion 0.00 4.00 3.45 3.45 2.74 80.01 60.83 60.83 95.36
4. Conclusion
We have presented the required steps to analyze the punching cards
mechanism and obtain the kinematic parameters through grapho-analytical method
and SolidWorks Motion software. The numerical values calculated by grapho-
analytical method were compared in Table 3 with the SolidWorks Motion results.
The magnitudes of all results indicated a very good agreement with the values
obtained by analysis in SolidWorks Motion software.
References
[1] Cortada J.W., Before the Computer, IBM, NCR, Burroughs, & Remington
Rand & The Industry They Created, Princeton University Press, 2000. [2] Lubar S., Do Not Fold, Spindle or Mutilate. A Cultural History of the Punch
Card, Journal of American Culture, 1992, pp. 43- 55.
[3] Anghel St., Ianici S., Mecanisme plane articulate. Probleme applicative,
Editura Eftimie Murgu, Resita, 2001.
[4] Dassault Systems 2010 SolidWorks Motion, 300 Baker Avenue, Concord,
Massachusetts, 01742, 2010, USA.
[5] Nedelcu D., Nedeloni M.D., Daia D., The Kinematic and Dynamic Analysis of
the Crank Mechanism with SolidWorks Motion, Proceedings of the 11th
WSEAS International Conference on Signal Processing, Computational
Geometry and Artificial Vision, Italy, 23-25 August 2011, pp. 245-250.
Addresses:
• Prof. Dr. Eng. Dorian Nedelcu, “Eftimie Murgu” University of Reşiţa, Piaţa Traian Vuia, nr. 1-4, 320085, Reşiţa, [email protected]
• Prof. Dr. Eng. Gilbert-Rainer Gillich, “Eftimie Murgu” University of Reşiţa, Piaţa Traian Vuia, nr. 1-4, 320085, Reşiţa, [email protected]
• Prof. dr. Istvan Biro, Faculty of Engineering, University of Szeged, Mars tér 7, H-6724 Szeged, [email protected]
• Lect. Dr. Eng. Habil. Zoltan-Iosif Korka, “Eftimie Murgu” University of Reşiţa, Piaţa Traian Vuia, nr. 1-4, 320085, Reşiţa, [email protected]
• PhD student Attila Gerocs, “Eftimie Murgu” University of Reşiţa, Piaţa Traian Vuia, nr. 1-4, 320085, Reşiţa, [email protected]